Finite temperature properties of theSO(3) lattice gauge theory

Abstract

We make a numerical study of the finite temperature properties of the SO(3) lattice gauge theory. As its symmetry properties are quite different from those of the SU (2) LGT, a different set of observables has to be considered in this model. We study several observables, such as the plaquette square, the Z(2) monopole density, the fundamental and adjoint Wilson line, and the tiled Wilson line correlation function. Our simulations show that the Z(2) monopoles condense at strong coupling just as in the bulk system. This transition is seen at approximately the same location as in the bulk system. A surprising observation is the multiple valuedness of the adjoint Wilson line at high temperatures. At high temperatures, we observe long lived metastable states in which the adjoint Wilson line takes positive and negative values. The numerical values of other observables in these two states appear to be almost the same. We study these states using different methods and also make comparisons with the high temperature behavior of the SU (2) LGT. Finally, we discuss various interpretations of our results and point out their relevance for the phase diagram of the SO (3) LGT at finite temperature.

Comparison of SO(3) and SU(2) lattice gauge theory

“…4 For sufficiently large ε, lattice artifacts are completely suppressed and η µν = ±1. In this case, however, the modified Villain theory becomes equivalent to an SU(2) theory with plaquette restriction Tr F U p > ε, summed over all twist sectors.…”

“…A further peculiarity of the SO(3) theory is the occurance of a new meta-stable "phase" (long-lived state in the Monte-Carlo simulation) with a negative expectation value of the adjoint Polyakov loop at weak coupling [4,5]. Apart from the Polyakov loop, this "phase" seems to be very similar to the standard phase with positive adjoint Polyakov loop.…”

“…[4,5]. In these articles, SO(3) lattice gauge theory was studied with both the Wilson and the Villain action.…”

SO(3) Versus SU(2)Lattice Gauge Theory

“…Another feature of SO (3) encouraging such speculation is the existence of a "mysterious phase", reported by Datta and Gavai [11]. This phase appears in all respects similar to the "normal" phase, except for the Polyakov loop P : instead of 1 2 Tr F P approaching ±1 as β A → ∞, it approaches zero (so that, in the adjoint representation, Tr A P → −1 instead of +3).…”

“…Therefore, we deal with a genuine SO(3) action, which shows the same bulk first-order transition (at β V ≈ 4.47) and the same "mysterious phase" [11]. The advantage of the Villain choice is that the connection SO(3) ↔ SU (2) is easier to display.…”